Decay of polarized particle into two spinless

[moss]

Hi All, I want to understand the decay of a spin-1 massive vector particle into two spinless massive particles.

Given a massive vector particle V with spin Sz = +1, 0, -1 decays into 2 massive spinless particles. I have to compute the amplitude M but I don't know what should I do with the polarization vectors?

Hence my Qs. is that, does the Sz vectors becomes the polarization vectors?
is the angular momentum and/or Sz conserve?

I am kind of al-confuso because never did any polarized photon-less decay before.
any help is much appreciated.

 

[vanhees71]

Do you have a concrete model at hand? The calculation can be done in the usual way using Feynman rules. Usually you are interested in the unpolarized cross section, i.e., you average $|\mathcal{M}_{fi}|^2$ over the polarization states of the decaying vector particles in the initial state.

 

[moss]

Do you have a concrete model at hand? The calculation can be done in the usual way using Feynman rules. Usually you are interested in the unpolarized cross section, i.e., you average $|\mathcal{M}_{fi}|^2$ over the polarization states of the decaying vector particles in the initial state.

Thanks for the reply,
so e.g for Sz=1 what polarization vector should I use assuming the axis is z.?

 

[moss]

Okay the original Qs. with V=vector particle and S1 & S2 are spinless is that;

Let V--->S1S2 in the rest frame with S1 emitted in the x-z plane at and angle theta respect to z-axis.
show that the decay rates for polarization states of V with spin Sz=+1,-1,0 along the z-direction
are proportional to sin^2(theta) and cos^2(theta) respectively.